Analytical Solutions of the Schrödinger Equation with Class of Yukawa Potential for a Quarkonium System Via Series Expansion Method

Inyang, E. P.; Akpan, I. O.; Ntibi, Joseph E.; William, E. S.

doi:10.24018/ejphysics.2020.2.6.26

Cited by 37 publications

(24 citation statements)

References 16 publications

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“…We calculate the mass spectra of the heavy quarkonium system such as charmonium and bottomonium that have the quark and antiquark flavor, and apply the following relation [36,37]…”

Section: Resultsmentioning

confidence: 99%

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

2021

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Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

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“…We calculate the mass spectra of the heavy quarkonium system such as charmonium and bottomonium that have the quark and antiquark flavor, and apply the following relation [36,37]…”

Section: Resultsmentioning

confidence: 99%

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

2021

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show abstract

“…Using the relation in Refs. [36,37], we calculate the mass spectra of the heavy quarkonia such as charmonium and bottomonium.…”

Section: Resultsmentioning

confidence: 99%

Masses and thermodynamic properties of a quarkonium system

et al. 2021

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Hulthen plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmoniumand cc and bottomonium bb, and thermodynamic properties such as the mean energy, the specific heat, the free energy, and the entropy. Four special cases were considered when some of the potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulthen potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

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“…They found the energy and mass spectrum of heavy quarkonia [31]. Omugbe [31] applied the Nikiforov-Uvarov method to obtain the eigensolutions of the radial Schrödinger equation with Cornell potential plus an inversely quadratic potential [11,31,34]. Until now, an analysis of such states in quantum phase space via the Wigner function is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz

Petronilo

et al. 2022

Advances in High Energy Physics

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In this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the c c ¯ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, and the nonclassicality of ground state and first excited state is studied by the nonclassicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the nonclassic nature of meson system than the wavefunction does phase space.

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Analytical Solutions of the Schrödinger Equation with Class of Yukawa Potential for a Quarkonium System Via Series Expansion Method

Cited by 37 publications

References 16 publications

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

Masses and thermodynamic properties of a quarkonium system

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

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